ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   162.   79.1 Blue      
 2     2   185.   83.3 Green     
 3     3   176.   94.5 Brown     
 4     4   174.   86.4 Brown     
 5     5   175.   76.0 Green     
 6     6   162.   68.5 Grey      
 7     7   163.   80.1 Brown     
 8     8   158.   74.8 Grey      
 9     9   180.   89.0 Blue      
10    10   162.   81.2 Blue      
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1]  0.402606415 -1.098805035 -0.678908771  0.342489196  1.147744152
   [6] -0.452373946  1.386184102  0.795367447  0.407133305 -1.387912500
  [11] -0.480409260 -1.320078502 -1.662695374  1.245031745 -0.522889907
  [16] -0.456132135 -1.345289247 -1.122689141  0.969041079 -1.699843621
  [21] -1.856691623 -0.672086995 -0.980044405 -0.430955108  0.602497506
  [26] -0.382062508 -0.174714076 -1.469651375  0.482267657 -0.924285745
  [31]  0.074249553 -0.517265252 -0.437210011 -0.297440530  0.284486547
  [36] -1.590419861  0.342943711  0.136982829  1.259873382 -1.530430766
  [41]  0.081655526 -0.308960674 -0.286936540  0.979550284  0.496507688
  [46]  1.084705974 -2.248420105 -0.218435596 -0.875530352 -2.023383960
  [51]  0.384864879  0.386871757  0.521437574 -1.357794950 -0.948912671
  [56]  0.683236734  0.863986455 -0.288346632 -0.195799727  0.374877581
  [61]  0.087685357 -0.225759981  0.581026363  0.096848675  0.875518024
  [66] -0.293439414  0.776833874 -0.227719530  0.461611469  2.228068483
  [71]  0.384016839  0.456421379  0.113642621  1.497853833 -1.132833979
  [76] -0.094489006  1.502348284  0.368901916  0.160868798 -1.452347243
  [81]  0.665062359  0.147119154 -0.147565800  1.782630973  0.368367949
  [86] -0.337133262 -0.768866604  1.771109144 -0.066977881 -1.106586473
  [91] -1.351264884  0.689559920  0.885480006  0.042418792  1.543368524
  [96]  2.397220695  0.266559141  0.300606252  0.628554285 -0.555368231
 [101]  1.090625071 -0.643165505 -1.160935552 -0.001742840 -0.370732515
 [106]  0.531899857 -0.914467563 -0.877374883 -0.572801554 -0.238159184
 [111]  0.105850584  0.664564695  0.163641574  0.369437776  2.076509482
 [116]  0.063750817 -1.736458182 -0.864642052  0.287611018 -1.305610758
 [121] -1.561285388  0.729181169 -0.665107560 -0.261857518 -0.581260338
 [126] -1.301219524 -0.345659512 -1.857869723 -0.758138993  0.100599957
 [131]  0.819755816  0.108122639 -0.331943355 -0.935732665  1.007964363
 [136] -1.026166756 -0.167032414  0.999394789  1.241985271  0.032510183
 [141]  0.205215522 -2.061109716  0.725105861  1.286919450  0.003329972
 [146]  0.671456062 -0.167960232 -0.126402802 -0.487738335 -0.568780524
 [151]  1.663104975 -0.015869751 -0.798480800 -0.565337259  0.383962354
 [156]  0.120466636 -0.664478065 -0.701143457 -1.442131651  2.735962070
 [161]  0.340571488 -2.002298896  0.101892656  0.210449380  0.180856324
 [166]  0.053317371  0.716651369  1.292107094  0.238701967 -0.798363164
 [171] -0.948037461 -1.635290355  2.225226519 -0.172369730  1.266599612
 [176] -0.917484064  0.480640027 -0.447226725 -0.040199396  0.046300390
 [181] -0.144418521  0.552056499 -0.510129656  0.433831914  1.439631311
 [186] -1.216587048 -0.280119770  0.926443658  0.940842985  1.004119692
 [191]  0.266818281  1.057418476 -0.392937571  1.348318808 -0.692484005
 [196]  0.351252746  1.092175971  1.453735061 -0.725403986  0.342652574
 [201]  1.655462981  0.140200438 -0.141092857 -0.087463776  1.131627997
 [206] -2.621172979  1.246750676 -0.457663573 -0.639492276 -0.391608069
 [211] -0.180040495 -0.048527342  0.420209719 -1.376519563  0.132585287
 [216] -0.247831560 -0.770926046  1.895318074  1.340557553 -0.398750363
 [221] -1.310424277 -0.515682397  0.375456069 -0.061575592 -0.035280231
 [226] -0.923127534 -0.186101609 -0.403178337 -0.822736507 -0.803962096
 [231] -0.362481210  0.962891206  1.131960946  0.781151936  0.884201534
 [236]  1.426794539 -0.400030322  2.220932617 -1.939868654 -1.529584267
 [241]  0.525784443  1.129819859 -0.079378405 -1.258805359  0.097816457
 [246] -1.587102699  0.050879897  2.315193488 -0.469175825 -0.173711577
 [251] -1.756462994 -2.229869626  0.743033526  1.909819483  0.766028794
 [256]  1.458285659 -0.668182392  1.798997393  0.417903806 -2.121483997
 [261]  0.183661839 -1.887407710  0.090679230  0.764731973 -0.260330845
 [266] -0.046741164  0.002602240 -2.246675884 -0.615466072 -0.812550718
 [271] -0.516994986  0.232717940 -0.595156685 -0.700784020 -0.369483699
 [276]  0.233103300  0.472359721 -1.922958795  1.047603531  0.203738839
 [281]  1.257741565 -0.291645562  0.064235059 -1.347597684  1.415362450
 [286]  0.067712081  0.215671933 -0.168891842  0.143178257  0.102106829
 [291] -0.667420674 -0.120251052 -0.628575356  0.119231149 -0.572630684
 [296]  1.444579330 -0.937254034  0.399934122 -0.262579911  1.801878119
 [301]  2.120347632  1.341000672  0.878439895 -0.881408701 -0.132928690
 [306]  0.518073951 -0.255486675  0.535925879  0.308043652  1.914615473
 [311] -0.103493435 -0.142845702 -0.558002840 -0.466127074  0.602621055
 [316] -0.212961123 -2.519511493 -1.019610579  0.141179481  1.072637467
 [321] -0.950538992  0.430002264 -0.890209612 -0.854582987 -1.369052593
 [326]  0.821948583  0.845573561  0.363451885  0.721345100 -1.502433915
 [331]  0.171914871  0.742269745  1.702764826  1.624097214 -0.224125987
 [336] -0.532101937  0.198253551 -1.299031794 -0.959953666 -0.311962941
 [341] -0.179343252  0.385878650 -1.626604355  0.309982365 -0.253740887
 [346] -2.401266967  0.625514702  0.443985955 -2.096158189  0.140663033
 [351] -0.219426582  0.689182907  0.341861074 -1.286632057 -0.932971247
 [356]  1.170166546 -0.199926232 -1.472934144 -1.635247631 -0.160389097
 [361]  2.443058714  1.092932985  0.766115854  0.461498457 -0.171097963
 [366]  1.651862097 -2.266210475  1.035716990 -0.979199574 -0.192570207
 [371]  1.393681871  0.221207035 -1.183551504  1.352291069  0.664024237
 [376]  0.201791659 -0.793026428  1.980466586  1.239871643 -0.182560211
 [381]  1.644055430 -0.080405092  2.044193394  0.022899373 -0.536016035
 [386]  0.709900796 -0.526597960  0.934873248  1.215096486 -0.970095148
 [391]  0.051152828 -0.508501801  0.320581421  1.078703439  0.792275000
 [396] -2.240177011 -0.614721863  0.325074998 -1.609920871 -1.581497759
 [401]  1.599635015  1.080823267 -0.690287004 -0.533915078  0.603194624
 [406] -0.489120894 -0.270674619  0.066058916  0.914758716  2.224173466
 [411]  0.786917176 -0.878230775  1.357611021 -0.326525874 -0.813008890
 [416]  1.671656198 -0.651134323  0.845246574 -2.601987383  1.874210508
 [421]  0.726957623 -1.207189340  1.130040247  0.358815965 -0.318175436
 [426] -1.198748933  0.591357036 -1.826790544 -0.043036272 -0.395574219
 [431] -0.467406088  1.249936887 -1.002568361  1.728411558  0.621978612
 [436]  0.317657369  0.196502064  1.016095910 -0.030113619 -0.316284731
 [441] -1.470036783 -1.616320170 -0.836819223 -1.484210514  1.097408824
 [446] -0.316255081  0.550800543 -1.466149845  0.331149227 -0.875118318
 [451]  0.481201925  0.927872346  0.058151454  0.040814346  1.320671459
 [456]  1.172096137 -0.561767794  0.478459300 -0.970174940 -0.904386689
 [461] -0.574619031 -0.714777778  0.034239252 -0.226889418  1.591182834
 [466]  0.022025696 -1.809673494  1.128051432  0.787171688  1.058855708
 [471] -0.881581775 -1.445398905  0.333515836  0.020169919  1.206087562
 [476] -0.280617533 -0.499279678 -0.900970017  0.368738132 -0.055960420
 [481]  0.730698013  1.511399946 -0.212116257 -1.051942425 -0.299666803
 [486] -0.006019458  0.579481674  0.211975001 -1.345872712 -0.613755938
 [491]  0.169759119 -0.840412785 -0.726225163  0.326478171  1.166099174
 [496] -1.774665444 -0.654308446  0.050161906  0.900370889 -0.189799627
 [501] -0.492383409  0.045358134 -0.099593749  0.451591045 -1.092593992
 [506]  0.725843116 -2.062858817  1.144266632 -0.443583353 -1.862048808
 [511]  1.625503048  1.168487195  0.930492950 -0.371981729 -3.348996170
 [516] -0.690521548 -0.648185635 -1.525226757  0.627084544  0.439213027
 [521] -0.265265612 -1.399456634 -0.304958194 -0.209757261  1.159990934
 [526]  0.592474802  0.461422935 -1.669359851  0.829078576  1.005844264
 [531]  0.997587383 -2.444427461  2.026847901  0.821169227  1.250023221
 [536]  1.273735341 -1.141015435 -0.213344136 -2.127323841  0.489994430
 [541] -0.450316526 -0.977342118  0.579705239 -0.311938588  1.111953340
 [546]  0.066739900  1.366593814 -0.442967068  0.489821852  0.938534888
 [551]  1.843772350 -0.696963782  0.488128114  0.043653696  0.418738808
 [556]  1.366564714 -1.142562407  0.312176798 -0.397432213 -0.263850683
 [561]  0.965093008  0.549062376 -0.452808387  1.067911235  0.347418235
 [566] -0.752365944 -0.571235942 -1.000823271  0.787026057  1.044918221
 [571]  0.267508941  0.006626084 -0.771530273  0.244057735  0.563077168
 [576] -1.322893711 -1.327995988  1.441962334 -1.408345521 -0.430830285
 [581]  0.852708936  1.758922710  0.916545454  2.210001380  0.444543975
 [586] -0.414493783  0.873440969  0.262436071 -0.521644135 -0.694004909
 [591] -0.816021889  0.869706371  0.197113788  0.491927144  0.285894001
 [596] -0.154853713  0.099375425  2.340210542  0.773288006 -0.137174081
 [601] -0.108152609 -0.664840037  0.210241578 -1.426162953  1.028814804
 [606]  0.767834959  2.108419624 -0.791212560 -1.161250205 -0.149982466
 [611]  0.045313368  0.673470793  1.270294750  1.514130451  0.695271631
 [616] -0.956679497  0.957474017 -0.132386859  0.038927441  0.330977240
 [621]  1.227379568  0.289602288  0.145245535 -0.352711329  0.136908158
 [626]  0.185564284  0.918652158  1.100275289 -0.182229408  2.402254762
 [631]  1.751493850 -0.888636851  0.904109462  0.254881371 -0.671770881
 [636] -1.417195651  0.801260885 -0.802234694  0.197031800  1.607826911
 [641] -0.356128708  3.526458878  0.443254203 -1.773780813  0.379726794
 [646]  1.143832564  0.389297483 -0.352398389 -0.644944173  2.011661315
 [651]  2.668669311  0.179113536  1.070193750  0.992945992  0.604556779
 [656] -0.013620922  0.707140269  0.517935518 -0.425171415  0.460403646
 [661]  0.583151359  0.459657734 -0.311403491  1.124733667  1.396032652
 [666]  0.008780967  2.471462911 -1.020086785  0.540728703 -1.410142541
 [671]  0.783215031  0.011841691 -0.344357473  1.122666096 -0.499745335
 [676]  0.081700656 -0.238652222  2.542775889 -0.244492571 -1.562898853
 [681]  1.279868944  0.115369328  0.184153582 -1.557633475 -0.238473323
 [686] -0.350408977  0.526810246  1.446047971 -0.404778748 -1.253601690
 [691] -0.465124120  0.246014224  0.459496034 -0.212197785  0.273866643
 [696]  0.620890740 -0.283564462  0.914141114  0.309548260 -1.235355008
 [701] -0.555566527  1.351173125 -0.200818257  1.513306404  0.524511411
 [706] -0.089408310 -0.131046147  0.052890053  1.022497664  2.180734811
 [711]  2.931672985 -0.178773808  0.393461275  0.753156108  0.118287922
 [716] -0.251148543  0.403556933 -0.522888929  1.497022563 -0.927839191
 [721] -0.577956463  1.005996118 -0.024618648 -0.624184753 -0.372767455
 [726] -0.968480910  0.721244876  1.544773782 -0.025679132  0.488664075
 [731]  1.050558823 -1.740718897  1.187271239 -0.223401686 -0.090585106
 [736]  0.427079477  0.162714703  1.464237260 -1.084418331 -0.256925389
 [741]  0.611376400  1.193392912 -0.172251951 -0.007817152  0.111433434
 [746] -0.108854318 -0.083741509 -0.294377632 -0.140502580 -1.939934597
 [751]  0.909494934 -0.698517003  0.526113213 -1.441794788 -1.010294282
 [756] -0.486348236  0.407305746 -2.471061167 -0.588809663  0.416464774
 [761] -0.441811823  0.082893308  1.287485689  0.063267962 -0.882162704
 [766] -0.479955410 -1.070041644 -0.608201864 -0.840491505  0.327905195
 [771]  0.731877592 -1.060417946  0.164027263  1.008537688  0.059061395
 [776]  0.083176250 -0.284403797  1.218966112 -0.322047191 -1.158626859
 [781]  0.290098431 -1.118153223  0.550672591  0.846323151  0.242054369
 [786] -1.293340722 -1.293948042 -0.032290183  0.945518811  1.180222712
 [791] -1.455601148  0.412630255 -2.239087428  0.306894337 -0.645167077
 [796] -0.063927407  1.485505420  0.261495516 -1.704370831  0.144177486
 [801]  0.724456910 -0.643581668  0.149443915 -1.108643407 -0.028229658
 [806] -1.565081170  0.489215253 -0.127756137  0.405410731 -0.532193343
 [811]  0.602863550 -0.092943171 -0.054736479  0.140326501 -0.084420258
 [816]  1.234772881 -0.939637190  1.104809951  0.505404498 -0.605309017
 [821] -1.901623208 -0.624349740 -0.466475081 -3.043650874 -0.311286324
 [826] -0.080217233  0.822250119 -0.336672698  1.175615236  1.214442882
 [831]  0.442579517 -0.899329470  0.971688403  0.596526185  0.041074248
 [836] -0.814919134  2.088628882 -1.592567685 -1.105753581 -1.317286021
 [841]  0.305052070  0.199314705  1.055614174 -0.277027372 -0.084526228
 [846] -0.701019508  0.183774548 -0.316505572  0.352688823 -0.488916328
 [851]  0.157102405 -0.650826443 -0.079570593 -1.905122965 -0.030520499
 [856]  0.363015846 -1.221957056  1.378037764  0.773771316  1.295733793
 [861]  2.702726110  0.840004964 -0.001763807 -1.213814141  0.695508637
 [866] -1.671767635 -1.271709519  0.999688837 -0.019696204 -0.707670696
 [871]  1.492055069 -0.723893767 -0.760418283  0.086749809 -0.212475760
 [876]  0.017236474 -0.393975342  0.009427065  0.479899452  0.167458789
 [881] -0.829896694  0.234750239  1.513823482  0.962378662  0.303647261
 [886]  1.180576840  1.010855030 -0.873368611  1.515037971 -1.863089197
 [891]  1.082415509 -0.042771251 -0.263072822 -0.134276412  0.249750919
 [896]  0.163945127  1.459596975 -1.515658295 -0.381060738 -1.272815029
 [901]  1.675746121  0.326185667  0.076052697 -1.520495215 -0.528522975
 [906]  1.017690725  1.049173395 -0.573766166  0.670032532  0.046315012
 [911] -1.340945860  0.266337558  0.081099595  0.247103360 -0.322647307
 [916] -1.092179895  0.776269648  0.926298638 -0.296914055 -0.244848782
 [921]  0.521925227 -1.318372469 -0.708745526 -0.160692254 -0.833186726
 [926] -1.081207202 -0.568501378  0.178609137  0.752483729  0.828556150
 [931]  1.568815166 -2.211382748 -1.432125933  0.602474735 -0.939043703
 [936] -0.952316430 -0.593806204  0.888276448 -1.280665302 -1.212600511
 [941] -0.322817298  0.562644670 -0.628003698 -1.075560410 -1.465270628
 [946]  0.454405213 -0.031422665  0.792803200  0.129641844  0.691580246
 [951]  0.547564329  1.214000783 -0.072716847 -0.001846967 -0.471131749
 [956]  0.037300813  0.535813970  0.249334123 -1.750799205 -0.670844336
 [961]  1.257044415  0.450743542 -0.084951556 -2.354759382  0.146839180
 [966]  0.825502265  1.320408975  0.481632721  2.423766486  0.054540680
 [971] -0.482260807  1.244126316 -0.563966706  0.396252981  0.520549926
 [976]  0.290285103 -0.269426376  1.600642783  0.504233127  0.543506674
 [981]  1.412350980 -0.170416804 -0.176539611  0.588543157 -0.068554743
 [986] -0.613718016  0.686622794  0.611942608 -1.557108639 -0.506913227
 [991] -0.896022864 -0.364320753  0.197869314 -1.009999165 -0.883045266
 [996]  1.717810622  0.623361398  0.886747349  1.080752626  0.290748120

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1
  [38] 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0
  [75] 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0
 [112] 0 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0
 [149] 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1
 [186] 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1
 [223] 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1
 [260] 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 1
 [297] 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0
 [334] 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0
 [371] 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0
 [408] 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1
 [445] 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0
 [482] 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0
 [519] 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1
 [556] 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0
 [593] 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 0
 [630] 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1
 [667] 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1
 [704] 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0
 [741] 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0
 [778] 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0
 [815] 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1
 [852] 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1
 [889] 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0
 [926] 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 1
 [963] 0 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   162.   79.1 Blue       B    
 2     2   185.   83.3 Green      B    
 3     3   176.   94.5 Brown      A    
 4     4   174.   86.4 Brown      A    
 5     5   175.   76.0 Green      A    
 6     6   162.   68.5 Grey       A    
 7     7   163.   80.1 Brown      A    
 8     8   158.   74.8 Grey       A    
 9     9   180.   89.0 Blue       B    
10    10   162.   81.2 Blue       B    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups